Unsteady analysis for oscillatory flow of magnetorheological fluid dampers based on Bingham plastic and Herschel–Bulkley models

It is known that a quasi-static analysis without considering fluid inertia is usually used for magnetorheological damper design. However, fluid inertia terms need to be incorporated into the governing Navier–Stokes equation in practical application for oscillatory or unsteady fluid flow. In this article, an unsteady flow of magnetorheological fluids within flow mode magnetorheological dampers was theoretically investigated under sinusoidal displacement excitation. Based on the governing Navier–Stokes equation, incorporating the boundary and initial conditions, central numerical velocity solutions of magnetorheological fluids within magnetorheological damping channel were developed and used to confirm the damping force using both Bingham plastic and Herschel–Bulkley models of magnetorheological fluids. To simplify the governing equation of Herschel–Bulkley flow, an approximation method replacing Herschel–Bulkley model velocity with Bingham plastic model velocity during calculating effective viscosity shear rate of Herschel–Bulkley model is proposed and used. For given magnetorheological fluid properties and flow mode magnetorheological damper geometry, under different yield stresses, sinusoidal excitation frequencies, and power-law exponent of Herschel–Bulkley model, the effects of magnetorheological fluid inertia terms on work and characteristic diagrams of magnetorheological dampers are discussed.